Contact and Symplectic Geometry (2018)

  Convener(s)
Name:

Dr. Kashyap Rajeevsarathy

Dr. Dheeraj Kulkarni
Mailing Address:

Room No. 314, Academic Building 1,
IISER Bhopal, Bhopal Bypass Road, Bhauri,
Bhopal, Madhya Pradesh 462 066

 Room No. 314, Academic Building 1,
IISER Bhopal, Bhopal Bypass Road, Bhauri,
Bhopal, Madhya Pradesh 462 066
Email:

kashyap at iiserb.ac.in

dheeraj at iiserb.ac.in

Dates: 

Monday, December 3, 2018 - 09:00 to Friday, December 14, 2018 - 18:00

Venue: 

Venue Address: 

Dept. Of Mathematics,
Academic building 1, IISER Bhopal,
Bhauri, Bhopal bypass road.

Venue State: 

Venue City: 

PIN: 

462066

Chrono Order: 

299

Syllabus: 

Syllabus to be covered in terms of modules of 6 lectures each :

Name of the Speakers with affiliation.

No. of Lectures

Detailed Syllabus

Outstation Speakers

Dr. Somnath Basu, IISER Kolkata. (SB)

5 (1.5 hrs each) = 7.5 hrs

Knot Contact Homology, Cord Algebras.

Dr. Mahuya Datta, ISI Kolkata. (MD)

5 (1.5 hrs each) = 7.5 hr

Introduction to Contact Geometry, Eliashberg’s Theorem for classification of overtwisted contact structures in dimension three.

Dr. Ritwik Mukherjee, NISER Bhubaneshwar. (RM)

6 (1.5 hrs each) = 9.0 hrs

Introduction to J-holomorphic curves, Moduli Spaces of J-holomorphic curves, Gromov-Witten Invariants.

Dr. Sushmita Venugopalan, IMSc., Chennai. (SV)

5 (1.5 hrs each) = 7.5 hrs

Hamiltonian Floer Homology and Lagrangian Floer Homology. Proof of Arnold’s conjecture in some cases.

Local Speakers

Dr. D. Divakaran, IISER Bhopal. (DD)

4 (1.5 hrs each) = 6 hrs

Donaldson’s construction of Approximately Holomorphic sections, Existence of Symplectic Submanifolds, Lefschetz Pencils on symplectic 4-manifolds.

Dr. Atreyee Bhattacharya, IISER Bhopal. (AB)

3 (1.5 hrs each) +2 (1 hr each) = 6.5 hrs

Riemannian Geometry of Contact Manifolds, Contact Sphere Theorem. Some open problems in contact metric manifolds.

Dr. Anandateertha Mangasuli, IISER Bhopal. (AM)

3 (1.5 hrs each) + 2 (1 hr) = 6.5 hrs

Introduction to Symplectic Topology, Classical Mechanics and symplectic structures, Contact structures in PDE’s.

Dr. Kashyap Rajeevsarathy, IISER Bhopal. (KR)

2 (1.5 hrs each) = 3 hrs

Introduction to Mapping Class Groups, Primitivity of Mapping classes and contact structures

Dr. Dheeraj Kulkarni, IISER Bhopal. (DK)

2 (1.5 hrs each) = 3 hrs

Giroux correspondence relating open book decompositions and contact structures, Fillability of contact structures.

References:

Books:

  1. McDuff, Dusa, and Dietmar Salamon. Introduction to symplectic topology. Oxford University Press, 2017.

  2. McDuff, Dusa, and Dietmar Salamon. J-holomorphic curves and symplectic topology. Vol. 52. American Mathematical Soc., 2012.

  3. Geiges, Hansjörg. An introduction to contact topology. Vol. 109. Cambridge University Press, 2008.

  4. Farb, Benson, and Dan Margalit. A primer on mapping class groups (pms-49). Princeton University Press, 2011.

  5. Eliashberg, Yakov, and Nikolai M. Mishachev. Introduction to the h-principle. No. 48. American Mathematical Soc., 2002.

  6. Audin, Michèle, and Jacques Lafontaine, eds. Holomorphic curves in symplectic geometry. Vol. 117. Birkhäuser, 2012.

  7. Audin, Michèle, and Mihai Damian. Morse theory and Floer homology. London: Springer, 2014.

 Articles:

  1. Ekholm, Tobias, John B. Etnyre, Lenhard Ng, and Michael G. Sullivan. "Knot contact homology." Geometry & Topology 17, no. 2 (2013): 975-1112.

  2. Basu, Somnath, Jason McGibbon, Dennis Sullivan, and Michael Sullivan. "Transverse string topology and the cord algebra." arXiv preprint arXiv:1210.5722 (2012).

Time Table: 

Tentative time-table with names of the speakers and tutors with their affiliation:

Time

Lecture 1
9.30
to
11.00

Tea
11.05
to
11.25

 

Lecture 2
11.30
to
1.00

Lunch
1.00
to
2.00

 

Lecture 3
2.00
to
3.30

3.35
to
3.55

 

Discussion
4.00
to
5.00

5.05
to
5.35

 

 Day/Date

(name of the speaker)

(name of the speaker)

(name of the speaker)

(Name of the speaker/tutor)

Mon
3/12/2018

Introduction to Symplectic Geometry-I. (AM)

 T

E

A

Introduction to Contact Geometry- I . (MD)

L

U

N

C

H

Introduction to J-holomrophic curves-I. (RM)

T

E

A

Symplectic structures and Classical Mechanics (AM)

S

N

A

C

K

S

Tue
4/12/2018

Introduction to Symplectic Geometry-II. (AM)

Introduction to Contact Geometry-II. (MD)

Introduction to J-holomrophic curves-II. (RM)

Contact Structures in PDEs (AM)

Wed
5/12/2018

Introduction to Symplectic Geometry-III. (AM)

Introduction to Contact Geometry-III. (MD)

Introduction to J-holomrophic curves-III. (RM)

Reeb Flow and geodesic flow. (AB)

Thu
6/12/2018

Introduction to Mapping Class groups. (KR)

The Giroux Correspondence. (DK)

Moduli Spaces Of J-holomorphic curves-IV. (RM)

Gromov’s Compactness - I (1.5 hrs) (DD)

Fri
7/12/2018

Approximately Holomorphic Geometry (DD)

Eliashberg’s Classification of Overtwisted Contact Structures in dimension 3. Part-1 (MD)

Gromov-Witten Invariants, Enumerative Geometry (RM)

Gromov’s Compactness - II. (1.5 hrs) (DD)

Sat
8/12/2018

Approximately Holomorphic Geometry (DD)

Eliashberg’s Classification of Overtwisted Contact Structures in dimension 3.Part-2. (MD)

Gromov-Witten Invariants, Enumerative Geometry (RM)

Enumerative Geometry

Mon
10/12/2018

Knot Contact homology (SB)

Open Books and Fillability of contact structures. (DK)

Arnold’s Conjecture and Floer Theories (SV)

Primitivity in the mapping class group and related open problems. (KR)

Tue
11/12/2018

Knot Contact homology (SB)

Riemannian geometry of Contact manifolds. (AB)

Arnold’s Conjecture and Floer Theories (SV)

Open Problems in Riemannian geometry of Contact manifolds (AB)

Wed
12/12/2018

Knot Contact homology (SB)

Riemannian geometry of Contact manifolds. (AB)

Arnold’s Conjecture and Floer Theories (SV)

Open Problems in Rigidity Side of Symplectic and Contact Structures.

Thu
13/12/2018

Knot Contact homology (SB)

Riemannian geometry of Contact manifolds. (AB)

Arnold’s Conjecture and Floer Theories (SV)

Open Problems in Rigidity Side of Symplectic and Contact Structures.

Fri
14/12/2018

Knot Contact homology (SB)

Arnold’s Conjecture and Floer Theories (SV)

Conclusion.

 

Selected Applicants: 

 

Sr.n SID Full Name Gender

Affiliation

 Position in College/ University University/ Institute M.Sc./M.A. Year of Passing M.Sc. /M.A Ph.D. Degree Date
1 21869 Mr. Dibakar Dey Male University of Calcutta Ph.D Student University of Calcutta 2017  
2 22331 Mr. Rahul Raju Pattar Male Sri Sathya Sai Institute of Higher Learning PhD Sri Sathya Sai Institute of Higher Learning 2017  
3 22380 Mr. Umar Mohammad Khan Male Aligarh Muslim University PhD Student Aligarh Muslim University 2015  
4 22902 Mr Anantadulal Paul Male NISER PhD University Of Pune(S.P.P.U), Pune 2015  
5 22961 Mr Selvakumar A Male IIT, Madras PhD Ayya Nadar Janaki Ammal College, Sivakasi 2015  
6 22962 Mr. Abhijeet Atmaram Ghanwat Male Chennai Mathematical Institute, Chennai Ph.D. Student University Of Pune, Pune 2014  
7 22964 Mr. Aritra Bhowmick Male Indian Statistical Institute, Kolkata PhD Indian Institute of Technology, Kanpur 2015  
8 22987 Mr Arijit Nath Male IIT Madras Ph.D Student Ramakrishna Mission Vivekanada University 2013  
9 23040 Dr. Rahul Kumar Singh Male NISER Bhubaneshwar Post Doctoral Fellow M. S. University of Baroda 2009 9/19/2017
10 23091 Mr. Nilkantha Das Male NISER Bhubaneshwar PhD IIT BOMBAY 2016  
11 23168 Mr. Sachchidanand Prasad Male Indian Institute of Science Education and Research, Kolkata PhD NIT Rourkela 2017  
12 23294 Mr. Sambit Senapati Male Chennai Mathematical Institute MSc Student      
13 23324 Dr. Dhriti Sundar Patra Male BIT Mesra Assistant Professor IIT Bombay 2011 11/10/2017
14 23328 Mr. Paramjit Singh Male Chennai Mathematical Institute MSc Student Chennai Mathematical Institute    
15 23340 Mr. Sourav Ghosh Male Chennai Mathematical Institute MSc Student Chennai Mathematical Institute    
16 23348 Mr. Puneet Kumar Gupt Male University of Lucknow, Lucknow PhD University of Lucknow, Lucknow 2012  
17 23374 Mr. Satyajit Maity Male IISER Mohali Visiting for a reading project (unofficial) CMI 2018  
18 23381 Mr Jagadish Pine Male CMI Research Scholar Presidency University 2016  
19 23404 Mr. Somrik Bhattacharya Male Techno India University MSc Student Techno India University    
20 23436 Mr. Neeraj Kumar Dhanwani Male IISER Bhopal Ph.D. Devi Ahiliya University 2015  
21 23438 Mr. Suprokash Hazra Male IISER Bhopal PhD student Pondicherry University 2016  
22 23446 Mr. Ranadip Gangopadhyay Male Banaras Hindu University PhD student Netaji Subhas Open University 2013  
23 23453 Mr. Sannidhi Alape Male Indian Institute of Science Education and Research Bhopal PhD Chennai Mathematical Institute 2016  
24 23462 Mr. Joji Benny Male Indian Institute if Technology, Madras PhD student UM DAE CEBS 2016  
25 23466 Dr Avijit Sarkar Male University of Kalyani Assistant Professor University of Kalyani 2002 2/3/2010
26 23499 Mr. Sudeep Podder Male Indian Institute of Technology Madras Ph.D Ramakrishna Mission Vivekananda University 2017  
27 23501 Mr. Subhankar Sau Male IIT Madras Ph.D. IIT Madras 2017  

How to Reach: 

To Be Updated

School Short Name: 

csg

Last Date Application: 

Sunday, September 30, 2018

List of Conveners: 

Dr. Kashyap Rajeevsarathy
Dr. Dheeraj Kulkarni

School Type: 

NCMW